Two-loop renormalization group analysis of supersymmetric SO(10) models with an intermediate scale

Higher order corrections and unification in the minimal supersymmetric standard model: SOFTSUSY3.5

We present a renormalizable non supersymmetric Grand Unified SO(10) model which, at the price of a large fine tuning, is compatible with all compelling phenomenological requirements below the unification scale and thus realizes a minimal extension of the SM, unified in SO(10) and describing all known physics below M GUT. These requirements include coupling unification at a large enough scale to be compatible with the bounds on proton decay; a Yukawa sector in agreement with all the data on quark and lepton masses and mixings and with leptogenesis as the origin of the baryon asymmetry of the Universe; an axion arising from the Higgs sector of the model, suitable to solve the strong CP problem and to account for the observed amount of Dark Matter. The above constraints imposed by the data are very stringent and single out a particular breaking chain with the Pati-Salam group at an intermediate scale M I ~ 1011 GeV.

Calculating fermion masses in superstring derived standard-like models

$\mu$-$\tau$ symmetry imposed on the neutrino mass matrix in the flavour basis is known to be quite predictive. We integrate this very specific neutrino symmetry into a more general framework based on the supersymmetric SO(10) grand unified theory. As in several other models, the fermion mass spectrum is determined by Hermitian mass matrices resulting from the renormalizable Yukawa couplings of the 16-plet of fermions with the Higgs fields transforming as $10, \bar{126},120$ representations of the SO(10) group. The $\mu$-$\tau$ symmetry is spontaneously broken through the 120-plet. Consequences of this scheme are considered for fermion masses using both type-I and type-II seesaw mechanism. This scenario is shown to lead to a generalized CP invariance of the mass matrices and vanishing CP violating phases if the Yukawa couplings are invariant under the $\mu$-$\tau$ symmetry. Small explicit breaking of the $\mu$-$\tau$ symmetry is then shown to provide a very good understanding of all the fermion masses and mixing. Detailed fits to the fermion spectrum are presented in several scenarios. One obtains a very good fit to all observables in the context of the type-I seesaw mechanism but type-II seesaw model also provides a good description except for the overall scale of the neutrino masses. Three major predictions on the leptonic mixing parameters in the type-I seesaw case are (1) the atmospheric mixing angle $\theta_{23}^{l}$ close to maximal, (2) $\theta_{13}^{l}$ close to the present upper bound and (3) negative but very small Dirac CP violating phase in the neutrino oscillations.

We give an explicit formula for the proton decay rate in the minimal renormalizable supersymmetric (SUSY) SO(10) model. In this model, the Higgs fields consist of the 10 and $\mathbf{\overline{126}}$ SO(10) representations in the Yukawa interactions with matter and of the 10, $\mathbf{\overline{126}}$ , 126, and 210 representations in the Higgs potential. We present all the mass matrices for the Higgs fields contained in this minimal SUSY SO(10) model. Finally, we discuss the threshold effects of these Higgs fields on the gauge coupling unification.

In the minimal supersymmetric standard model (MSSM) contained in SUSY SO(10), top-\(b\)-\(\tau\) Yukawa unification is achieved at the intermediate mass scale \(M_I\simeq 10^{13.10}\) GeV using the recent world average experimental value of the top-quark mass, \(m_{\rm top} = 175\pm 6\) GeV, which has been directly established by CDF and D0 experiments at the Tevatron Collider. It is also observed that the Yukawa couplings unification scale \(M_I\) can be further decreased by taking lower input values of the top-quark mass. This trend indicates the possible existence of an intermediate symmetry breaking scale in SUSY SO(10). The present finding does not agree with the earlier notion that the third generation Yukawa couplings unification should occur at the GUT scale \(M_U\).

We study Higgs boson production associated with single top or anti-top via t-channel weak boson exchange at the LHC. The process is an ideal probe of the top quark Yukawa coupling, because we can measure the relative phase of htt and hWW couplings, thanks to the significant interference between the two amplitudes. By choosing the emitted W momentum along the polar axis in the th ( overline{t}h ) rest frame, we obtain the helicity amplitudes for all the contributing subprocesses analytically, with possible CP phase of the Yukawa coupling. We study the azimuthal asymmetry between the W emission and the Wb ( overline{b} ) → t( overline{t} ) h scattering planes, as well as several t and overline{t} polarization asymmetries as a signal of CP violating phase in the htt coupling. Both the azimuthal asymmetry and the polarization perpendicular to the scattering plane are found to have the opposite sign between the top and anti-top events. We identify the origin of the sign of asymmetries, and propose the possibility of direct CP violation test in pp collisions by comparing the top and anti-top polarization at the LHC.

The clockwork is an extra-dimensional set-up for generating light particles with exponentially suppressed or hierarchical couplings of light particles with N massive states having comparable masses near the threshold scale of the mechanism in theories which contain no small parameters at the fundamental level. We explore the prospect of charged lepton flavour violation (cLFV) in a clockwork framework which encompasses Dirac mass terms as well as Majorana mass terms for the new clockwork fermions. We deive the masses of the non zero clockwork Majorana masses, and new particles in a clockwork framework and for their Yukawa couplings to the lepton doublets, in the framework where the clockwork parameters are universal. When the new clockwork Majorana masses are non zero, neutrino masses are generated as a result from the exchange of heavy messenger particles such as right handed iso$-$singlet neutrinos or iso$ - $triplet scalar bosons known as the seesaw mechanism. In the case of non zero clockwork Majorana masses, owing to the sizable effective Yukawa couplings of the higher mass modes neutrino masses can only be made tiny by conjecturing large Majorana mass in the teraelectron volt range for allthe clockwork gears. This is apparent from the constraints on the mass scale of the clockwork fermions due to the non-observation of the rare cLFV decay $ \mu\rightarrow e\gamma $, $ \tau \rightarrow \mu \gamma $, $ \tau\rightarrow e\gamma $. A general description of the clockwork mechanism valid for fermions, gauge bosons, and gravitons is discussed here. This mechanism can be implemented with a discrete set of new fields or, in its continuum version, through an extra spatial dimension.

We perform a preliminary study of the ability of the Higgs decay to four leptons to shed light on the top quark Yukawa couplings. In particular we examine whether the $h\to 4\ell$ `golden channel' is sensitive to the $CP$ properties of the top quark couplings to the Higgs boson. We show that kinematic distributions are sensitive to interference of the next-to-leading order electroweak corrections with the tree level $ZZ$ contribution. This translates into a sensitivity to the top quark Yukawa couplings such that meaningful constraints on their $CP$ properties can begin to be obtained once $\sim 300$ fb$^{-1}$ of data has been collected at $\sim 14$ TeV, with significant improvements at higher luminosity or with a higher energy hadron collider. This makes the $h\to4\ell$ channel a useful probe of the top quark Yukawa couplings that is qualitatively different from already established searches in $h\to V\gamma$ two body decays, $tth$, and $gg\to h$. We also briefly discuss other potential possibilities for probing the top Yukawa $CP$ properties in $h\to2\ell\gamma$ and $\ell^+\ell^-\to h Z, h\gamma$.

We consider the full genuine next-to-leading order SUSY–QCD corrections to the charged Higgs decays into quarks supplemented by the NNLO corrections to the effective top and bottom Yukawa couplings. The NNLO corrections to the effective top Yukawa coupling are a new ingredient of our analysis. We arrive at an approximate NNLO prediction for MSSM charged Higgs decays after including the N4LO QCD corrections for large charged Higgs masses. The residual uncertainties are in the percent range or below, depending on the particular MSSM scenario.

We study the renormalization group evolution and infrared stable fixed points of the Yukawa couplings and the soft supersymmetry breaking trilinear couplings of the minimal supersymmetric standard model with baryon and lepton number (and R-parity) violation involving the heaviest generations. We show analytically that in the Yukawa sector there is only one infrared stable fixed point. This corresponds to nontrivial fixed point for the top-, bottom-quark Yukawa couplings and the B violating coupling ${\ensuremath{\lambda}}_{233}^{\ensuremath{''}},$ and a trivial one for the $\ensuremath{\tau}$-Yukawa coupling. All other possible fixed points are either unphysical or unstable in the infrared region. We then carry out an analysis of the renormalization group equations for the soft supersymmetry breaking trilinear couplings, and determine the corresponding fixed points for these couplings. We also study the quasi-fixed-point behavior, both algebraically and with numerical solutions of the evolution equations, of the third generation Yukawa couplings and the baryon number violating coupling, and those of the soft supersymmetry breaking trilinear couplings. From the analysis of the fixed point behavior, we obtain upper and lower bounds on the baryon number violating coupling ${\ensuremath{\lambda}}_{233}^{\ensuremath{''}},$ as well as on the supersymmetry breaking trilinear couplings.

Chaotic inflation and a radiatively generated intermediate scale in the supersymmetric standard model

One-loop corrections to the top, stop and gluino masses in the MSSM

Quark–lepton unification and eight-fold ambiguity in the left–right symmetric seesaw mechanism

We examine a superpotential for an SO(10) GUT and show that if the parameters of the superpotential are in a certain region, the SO(10) GUT has an intermediate symmetry SU(2${)}_{\mathit{L}}$\ensuremath{\bigotimes}SU(2${)}_{\mathit{R}}$\ensuremath{\bigotimes}SU(3${)}_{\mathit{C}}$\ensuremath{\bigotimes}U(1${)}_{\mathit{B}\mathrm{\ensuremath{-}}\mathit{L}}$ which breaks down to the group of the standard model at an intermediate scale ${10}^{10}$--${10}^{12}$ GeV. In the model, by the breakdown of the symmetry, right-handed neutrinos acquire a mass of the intermediate scale through a renormalizable Yukawa coupling. \textcopyright{} 1996 The American Physical Society.